We present a novel approach for kinetic, spectral and chromatographic resolution of trilinear data sets acquired from slow chemical reaction processes via repeated chromatographic analysis with diode array detection. The method is based on fitting rate constants of distinct chemical model reactions (hard-modelled, integrated rate laws) by a Newton-Gauss-Levenberg/Marquardt (NGL/M) optimization in combination with principal component analysis (PCA) and/or evolving factor analysis (EFA), both known as powerful methods from bilinear data analysis. We call our method hard-modelled trilinear decomposition (HTD). Compared with classical bilinear hard-modelled kinetic data analysis, the additional chromatographic resolution leads to two major advantages: (1) the differentiation of indistinguishable rate laws, as they can occur in consecutive first-order reactions; and (2) the circumvention of many problems due to rank deficiencies in the kinetic concentration profiles. In this paper we present the theoretical background of the algorithm and discuss selected chemical rate laws.